Cell poking: quantitative analysis of indentation of thick viscoelastic layers

In Vitro Measurements of Cellular Forces and their Importance in the Lung-From the Sub- to the Multicellular Scale

Throughout life, the body is subjected to various mechanical forces on the organ, tissue, and cellular level. Mechanical stimuli are essential for organ development and function. One organ whose function depends on the tightly connected interplay between mechanical cell properties, biochemical signaling, and external forces is the lung. However, altered mechanical properties or excessive mechanical forces can also drive the onset and progression of severe pulmonary diseases. Characterizing the mechanical properties and forces that affect cell and tissue function is therefore necessary for understanding physiological and pathophysiological mechanisms. In recent years, multiple methods have been developed for cellular force measurements at multiple length scales, from subcellular forces to measuring the collective behavior of heterogeneous cellular networks. In this short review, we give a brief overview of the mechanical forces at play on the cellular level in the lung. We then focus on the technological aspects of measuring cellular forces at many length scales. We describe tools with a subcellular resolution and elaborate measurement techniques for collective multicellular units. Many of the technologies described are by no means restricted to lung research and have already been applied successfully to cells from various other tissues. However, integrating the knowledge gained from these multi-scale measurements in a unifying framework is still a major future challenge.

Characterizing carrier transport in nanostructured materials by force-resolved microprobing

The advent of novel nanostructured materials has enabled wearable and 3D electronics. Unfortunately, their characterization represents new challenges that are not encountered in conventional electronic materials, such as limited mechanical strength, complex morphology and variability of properties. We here demonstrate that force-resolved measurements can overcome these issues and open up routes for new applications. First, the contact resistance to 2D materials was found to be sensitively depending on the contact force and, by optimizing this parameter, reliable contacts could be repeatably formed without damage to the fragile material. Moreover, resistance of three-dimensional surfaces could be investigated with high accuracy in spatial position and signal through a force-feedback scheme. This force-feedback approach furthermore permitted large-scale statistical characterization of mobility and doping of 2D materials in a desktop-sized automatic probing system that fits into glove boxes and vacuum enclosures using easily available and low-cost components. Finally, force-sensitive measurements enable characterization of complex electronic properties with high lateral resolution. To illustrate this ability, the spatial variation of a surface’s electrochemical response was investigated by scanning a single electrolyte drop across the sample.

Mutation in the Core Structure of Desmin Intermediate Filaments Affects Myoblast Elasticity

Elastic properties of cells are mainly derived from the actin cytoskeleton. However, intermediate filaments are emerging as major contributors to the mechanical properties of cells. Using atomic force microscopy, we studied the elasticity of mouse myoblasts expressing a mutant form of the gene encoding for desmin intermediate filaments, p.D399Y. This variant produces desmin aggregates, the main pathological symptom of myofibrillar myopathies. Here we show that desmin-mutated cells display a 39% increased median elastic modulus compared to wild-type cells. Desmin-mutated cells required higher forces than wild-type cells to reach high indentation depths, where desmin intermediate filaments are typically located. In addition, heat-shock treatment increased the proportion of cells with aggregates and induced a secondary peak in the distribution of Young's moduli. By performing atomic force microscopy mechanical mapping combined with fluorescence microscopy, we show that higher Young's moduli were measured where desmin aggregates were located, indicating that desmin aggregates are rigid. Therefore, we provide evidence that p.D399Y stiffens mouse myoblasts. Based on these results, we suggest that p.D399Y-related myofibrillar myopathy is at least partly due to altered mechanical properties at the single-cell scale, which are propagated to the tissue scale.

Obtaining full contact for measuring polydimethylsiloxane mechanical properties with flat punch nanoindentation

Procedure to establish full contact between the sample and the 1 mm diameter cylindrical flat punch tip to measure polydimethylsiloxane (PDMS) mechanical properties using the Hysitron TriboIndenter is described. This procedure differs from the standard automated indentation because each indent has to be performed manually after establishing full contact with the sample surface. Incomplete contact happens because of the sample tilt with respect to the flat punch surface and results in incorrect elastic modulus values.•Automated indentation results in incorrect values of the elastic modulus due to initial incomplete contact between the flat punch and the PDMS sample surface, caused by the tilt, and using the unloading slope, which is affected by viscoelastic soft polymer deformation.•Correct procedure requires establishing the full contact between the tip and the sample. This is achieved by moving the tip into the sample in 1-2 μm increments, up to 40-80 μm maximum combined displacement, until the loading stiffness no longer increases.•The elastic modulus is calculated from the loading stiffness and the diameter of the flat punch, instead of the unloading stiffness, which is larger due to viscoelastic unloading. After establishing the full contact, other mechanical testing can be conducted.

Probing softness of the parietal pleural surface at the micron scale

The pleural surfaces of the chest wall and lung slide against each other, lubricated by pleural fluid. During sliding motion of soft tissues, shear induced hydrodynamic pressure deforms the surfaces, promoting uniformity of the fluid layer thickness, thereby reducing friction. To assess pleural deformability at length scales comparable to pleural fluid thickness, we measured the modulus of the parietal pleura of rat chest wall using atomic force microscopy (AFM) to indent the pleural surface with spheres (radius 2.5 and 5 μm). The pleura exhibited two distinct indentation responses depending on location, reflecting either homogeneous or significantly heterogeneous tissue properties. We found an elastic modulus of 0.38-0.95 kPa, lower than the values measured using flat-ended cylinders >100 μm radii (Gouldstone et al., 2003, Journal of Applied Physiology 95, 2345-2349). Interestingly, the pleura exhibited a three-fold higher modulus when probed using 2.5 vs. 5 μm spherical tips at the same normalized depth, confirming depth dependent inhomogeneous elastic properties. The observed softness of the pleura supports the hypothesis that unevenness of the pleural surface on this scale is smoothed by local hydrodynamic pressure.

Micromechanical regulation in cardiac myocytes and fibroblasts: implications for tissue remodeling

Cells of the myocardium are at home in one of the most mechanically dynamic environments in the body. At the cellular level, pulsatile stimuli of chamber filling and emptying are experienced as cyclic strains (relative deformation) and stresses (force per unit area). The intrinsic characteristics of tension-generating myocytes and fibroblasts thus have a continuous mechanical interplay with their extrinsic surroundings. This review explores the ways that the micromechanics at the scale of single cardiac myocytes and fibroblasts have been measured, modeled, and recapitulated in vitro in the context of adaptation. Both types of cardiac cells respond to externally applied strain, and many of the intracellular mechanosensing pathways have been identified with the careful manipulation of experimental variables. In addition to strain, the extent of loading in myocytes and fibroblasts is also regulated by cues from the microenvironment such as substrate surface chemistry, stiffness, and topography. Combinations of these structural cues in three dimensions are needed to mimic the micromechanical complexity derived from the extracellular matrix of the developing, healthy, or pathophysiologic heart. An understanding of cardiac cell micromechanics can therefore inform the design and composition of tissue engineering scaffolds or stem cell niches for future applications in regenerative medicine.

Estimation of cell Young's modulus of adherent cells probed by optical and magnetic tweezers: influence of cell thickness and bead immersion

A precise characterization of cell elastic properties is crucial for understanding the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular functions. Optical and magnetic tweezers are micromanipulation techniques which are widely used for quantifying the stiffness of adherent cells from their response to an external force applied on a bead partially embedded within the cell cortex. However, the relationships between imposed external force and resulting bead translation or rotation obtained from these experimental techniques only characterize the apparent cell stiffness. Indeed, the value of the estimated apparent cell stiffness integrates the effect of different geometrical parameters, the most important being the bead embedding angle 2gamma, bead radius R, and cell height h. In this paper, a three-dimensional finite element analysis was used to compute the cell mechanical response to applied force in tweezer experiments and to explicit the correcting functions which have to be used in order to infer the intrinsic cell Young's modulus from the apparent elasticity modulus. Our analysis, performed for an extensive set of values of gamma, h, and R, shows that the most relevant parameters for computing the correcting functions are the embedding half angle gamma and the ratio h(u)/2R, where h(u) is the under bead cell thickness. This paper provides original analytical expressions of these correcting functions as well as the critical values of the cell thickness below which corrections of the apparent modulus are necessary to get an accurate value of cell Young's modulus. Moreover, considering these results and taking benefit of previous results obtained on the estimation of cell Young's modulus of adherent cells probed by magnetic twisting cytometry (MTC) (Ohayon, J., and Tracqui, P., 2005, Ann. Biomed. Eng., 33, pp. 131-141), we were able to clarify and to solve the still unexplained discrepancies reported between estimations of elasticity modulus performed on the same cell type and probed with MTC and optical tweezers (OT). More generally, this study may strengthen the applicability of optical and magnetic tweezers techniques by insuring a more precise estimation of the intrinsic cell Young's modulus (CYM).

Acoustic microscope lens modeling and its application in determining biological cell properties from single- and multi-layered cell models

The acoustic microscopy technique provides some extraordinary advantages for determining mechanical properties of living cells. It is relatively fast, of excellent spatial resolution, and of minimal invasiveness. Sound velocity is a measure of the cell stiffness. Attenuation of cytoplasm is a measure of supramolecular interactions. These parameters are of crucial interest for studying cell motility and volume regulations and to establish the functional role of the various elements of the cytoskeleton. Using a scanning acoustic microscope, longitudinal wave speed, attenuation and thickness profile of a biological cell were measured earlier by Kundu et al. [Biophys. J. 78, 2270-2279 (2000)]. In that study it was assumed that the cell properties did not change through the cell thickness but could vary in the lateral direction. In that effort the acoustic-microscope-generated signal was modeled as a plane wave striking the cell at normal incidence. Such assumptions ignored the effect of cell inhomogenity and the surface skimming Rayleigh waves. In this paper a rigorous lens model, based on the DPSM (distributed point source method), is adopted. For the first time in the literature the cell is modeled here as a multi-layered material and the effect of some external drug stimuli on a living cell is studied.

Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy

OBJECTIVE

Articular chondrocytes respond to chemical and mechanical signals depending on their zone of origin with respect to distance from the tissue surface. However, little is known of the zonal variations in cellular mechanical properties in cartilage. The goal of this study was to determine the zonal variations in the elastic and viscoelastic properties of porcine chondrocytes using atomic force microscopy (AFM), and to validate this method against micropipette aspiration.

METHODS

A theoretical solution for stress relaxation of a viscoelastic, incompressible, isotropic surface indented with a hard, spherical indenter (5 microm diameter) was derived and fit to experimental stress-relaxation data for AFM indentation of chondrocytes isolated from the superficial or middle/deep zones of cartilage.

RESULTS

The instantaneous moduli of chondrocytes were 0.55+/-0.23 kPa for superficial cells (S) and 0.29+/-0.14 kPa for middle/deep cells (M/D) (P<0.0001), and the relaxed moduli were 0.31+/-0.15 kPa (S) and 0.17+/-0.09 kPa (M/D) (P<0.0001). The apparent viscosities were 1.15+/-0.66 kPas (S) and 0.61+/-0.69 kPa-s (M/D) (P<0.0001). Results from the micropipette aspiration test showed similar cell moduli but higher apparent viscosities, indicating that mechanical properties measured by these two techniques are similar.

CONCLUSION

Our findings suggest that chondrocyte biomechanical properties differ significantly with the zone of origin, consistent with previous studies showing zonal differences in chondrocyte biosynthetic activity and gene expression. Given the versatility and dynamic testing capabilities of AFM, the ability to conduct stress-relaxation measurements using this technique may provide further insight into the viscoelastic properties of isolated cells.

Probing single-cell micromechanics in vivo: the microrheology of C. elegans developing embryos

Cells are not directly accessible in vivo and therefore their mechanical properties cannot be measured by methods that require a direct contact between probe and cell. Here, we introduce a novel in vivo assay based on particle tracking microrheology whereby the extent and time-lag dependence of the mean squared displacements of thermally excited nanoparticles embedded within the cytoplasm of developing embryos reflect local viscoelastic properties. As a proof of principle, we probe local viscoelastic properties of the cytoplasm of developing Caenorhabditis elegans embryos. Our results indicate that unlike differentiated cells, the cytoplasm of these embryos does not exhibit measurable elasticity, but is highly viscous. Furthermore, the viscosity of the cytoplasm does not vary along the anterior-posterior axis of the embryo during the first cell division. These results support the hypothesis that the asymmetric positioning of the mitotic spindle stems from an asymmetric distribution of elementary force generators as opposed to asymmetric viscosity of the cytoplasm.

Measuring cell viscoelastic properties using a force-spectrometer: influence of protein-cytoplasm interactions

Cell adhesive and rheological properties play a very important role in cell transmigration through the endothelial barrier, in particular in the case of inflammation (leukocytes) or cancer metastasis (cancer cells). In order to characterize cell viscoelastic properties, we have designed a force spectrometer (AFM) which can stretch cells thereby allowing measurement of their rheological properties. This custom-made force spectrometer allows two different visualizations, one lateral and one from below. It allows investigation of the effects of rheology involved during cell stretching. To test the ability of our system to characterize such viscoelastic properties, ICAM-1 transfected CHO cells were analyzed. Two forms of ICAM-1 were tested; wild type ICAM-1, which can interact with the cytoskeleton, and a mutant form which lacks the cytoplasmic domain, and is unable to associate with the cytoskeleton. Stretching experiments carried out on these cells show the formation of long filaments. Using a previous model of filament elongation, we could determine the viscoelastic properties of a single cell. As expected, different viscoelastic components were found between the wild type and the mutant, which reveal that the presence of interactions between ICAM-1 and the cytoskeleton increases the stiffness of the cell.

Micromechanical coupling between cell surface receptors and RGD peptides

Contact between an adherent cell and the extracellular matrix (ECM) promotes the recruitment of structural and signaling molecules to the cytoplasmic domain of integrins, which mediate cell adhesion, cell migration, and cell growth. It is unclear whether the intracellular recruitment of these cytoplasmic molecules enhances the affinity between the ECM and the extracellular domain of the cell surface receptors (integrins). Using soft microneedles coated with Arg-Gly-Asp (RGD) peptides, a sequence commonly shared by ECM proteins, we apply a localized ramp shear stress to the surface of a HeLa cell and measure the cell stiffness and the collective (or apparent) unbinding lifetime of its surface receptors to RGD. These measurements demonstrate that both cell stiffness and the collective cell surface receptor-RGD unbinding lifetime increase with the duration of the pre-shear cell-microneedle contact and with the rate of shear applied to the cell membrane. These parameters are also crucially dependent on the integrity of the actin filament network. Our results are consistent with a model of positive feedback signaling where RGD-mediated initial recruitment of cytoskeletal proteins to the cytoplasmic domain of integrins directly enhances the interaction between the extracellular domain of integrins and the RGD sequence of ECM molecules.

Measurement of cell microrheology by magnetic twisting cytometry with frequency domain demodulation

Magnetic twisting cytometry (MTC) (Wang N, Butler JP, and Ingber DE, Science 260: 1124-1127, 1993) is a useful technique for probing cell micromechanics. The technique is based on twisting ligand-coated magnetic microbeads bound to membrane receptors and measuring the resulting bead rotation with a magnetometer. Owing to the low signal-to-noise ratio, however, the magnetic signal must be modulated, which is accomplished by spinning the sample at approximately 10 Hz. Present demodulation approaches limit the MTC range to frequencies <0.5 Hz. We propose a novel demodulation algorithm to expand the frequency range of MTC measurements to higher frequencies. The algorithm is based on coherent demodulation in the frequency domain, and its frequency range is limited only by the dynamic response of the magnetometer. Using the new algorithm, we measured the complex modulus of elasticity (G*) of cultured human bronchial epithelial cells (BEAS-2B) from 0.03 to 16 Hz. Cells were cultured in supplemented RPMI medium, and ferromagnetic beads (approximately 5 microm) coated with an RGD peptide were bound to the cell membrane. Both the storage (G', real part of G*) and loss (G", imaginary part of G*) moduli increased with frequency as omega(alpha) (2 pi x frequency) with alpha approximately equal to 1/4. The ratio G"/G' was approximately 0.5 and varied little with frequency. Thus the cells exhibited a predominantly elastic behavior with a weak power law of frequency and a nearly constant proportion of elastic vs. frictional stresses, implying that the mechanical behavior conformed to the so-called structural damping (or constant-phase) law (Maksym GN, Fabry B, Butler JP, Navajas D, Tschumperlin DJ, LaPorte JD, and Fredberg JJ, J Appl Physiol 89: 1619-1632, 2000). We conclude that frequency domain demodulation dramatically increases the frequency range that can be probed with MTC and reveals that the mechanics of these cells conforms to constant-phase behavior over a range of frequencies approaching three decades.

The effect of chitosan on stiffness and glycolytic activity of human bladder cells

The cell's cytoskeleton together with the cell membrane and numerous accessory proteins determines the mechanical properties of cell. Any factors influencing cell organization and structure can cause alterations in mechanical properties of cell (its ability for deformation and adhesion). The determination of the local elastic properties of cells in their culture conditions has opened the possibility for the measurement of the influence of different factors on the mechanical properties of the living cells. The effect of the chitosan on the stiffness of the non-malignant transitional epithelial cells of ureter (HCV 29) and the transitional cell cancer of urine bladder (T24) was determined using scanning force microscopy. The investigations were performed in the culture medium (RPMI 1640) containing 10% fetal calf serum in the presence of the microcrystalline chitosan of the three different deacetylation degrees. In parallel, the effect of chitosan on production of lactate and ATP level was determined. The results showed the strong correlation between the decrease of the energy production and the increase in Young's modulus values obtained for the cancer cells treated with chitosan.

Analysis of cell mechanics in single vinculin-deficient cells using a magnetic tweezer

A magnetic tweezer was constructed to apply controlled tensional forces (10 pN to greater than 1 nN) to transmembrane receptors via bound ligand-coated microbeadswhile optically measuring lateral bead displacements within individual cells. Use of this system with wild-type F9 embryonic carcinoma cells and cells from a vinculin knockout mouse F9 Vin (-/-) revealed much larger differences in the stiffness of the transmembrane integrin linkages to the cytoskeleton than previously reported using related techniques that measured average mechanical properties of large cell populations. The mechanical properties measured varied widely among cells, exhibiting an approximately log-normal distribution. The median lateral bead displacement was 2-fold larger in F9 Vin (-/-) cells compared to wild-type cells whereas the arithmetic mean displacement only increased by 37%. We conclude that vinculin serves a greater mechanical role in cells than previously reported and that this magnetic tweezer device may be useful for probing the molecular basis of cell mechanics within single cells.

Cell property determination from the acoustic microscope generated voltage versus frequency curves

Among the methods for the determination of mechanical properties of living cells acoustic microscopy provides some extraordinary advantages. It is relatively fast, of excellent spatial resolution and of minimal invasiveness. Sound velocity is a measure of the stiffness or Young's modulus of the cell. Attenuation of cytoplasm is a measure of supramolecular interactions. These parameters are of crucial interest for studies of cell motility, volume regulations and to establish the functional role of the various elements of the cytoskeleton. Using a phase and amplitude sensitive modulation of a scanning acoustic microscope (Hillman et al., 1994, J. Alloys Compounds. 211/212:625-627) longitudinal wave speed, attenuation and thickness profile of a biological cell are obtained from the voltage versus frequency or V(f) curves. A series of pictures, for instance in the frequency range 980-1100 MHz with an increment of 20 MHz, allows the experimental generation of V(f) curves for each pixel while keeping the lens-specimen distance unchanged. Both amplitude and phase values of the V(f) curves are used for obtaining the cell properties and the cell thickness profile. The theoretical analysis shows that the thin liquid layer, between the cell and the substrate, has a strong influence on the reflection coefficient and should not be ignored during the analysis. Cell properties, cell profile and the thickness of the thin liquid layer are obtained from the V(f) curves by the simplex inversion algorithm. The main advantages of this new method are that imaging can be done near the focal plane, therefore an optimal signal to noise ratio is achieved, no interference with Rayleigh waves occurs, and the method requires only an approximate estimate of the material properties of the solid substratum where the cells are growing on.

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.

Graphical method for force analysis: macromolecular mechanics with atomic force microscopy

We present a graphical method for a unifying, quantitative analysis of molecular bonding-force measurements by atomic force microscopy (AFM). The method is applied to interpreting a range of phenomena commonly observed in the experimental AFM measurements of noncovalent, weak bonds between biological macromolecules. The analysis suggests an energy landscape underlying the intermolecular force and demonstrates that many observations, such as "snaps-on," "jumps-off," and hysteresis loops, are different manifestations of a double-well energy landscape. The analysis gives concrete definitions for the operationally defined "attractive" and "adhesive" forces in terms of molecular parameters. It is shown that these operationally defined quantities are usually functions of the experimental setup, such as the stiffness of the force probe and the rate of its movement. The analysis reveals a mechanical instability due to the multistate nature of molecular interactions and provides new insight into macromolecular viscosity. The graphical method can equally be applied to a quantitative analysis of multiple unfolding of subunits of the giant muscle protein titin under AFM.

Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.

Characteristics of a membrane reservoir buffering membrane tension

When membrane-attached beads are pulled vertically by a laser tweezers, a membrane tube of constant diameter (tether) is formed. We found that the force on the bead (tether force) did not depend on tether length over a wide range of tether lengths, which indicates that a previously unidentified reservoir of membrane and not stretch of the plasma membrane provides the tether membrane. Plots of tether force vs. tether length have an initial phase, an elongation phase, and an exponential phase. During the major elongation phase, tether force is constant, buffered by the "membrane reservoir." Finally, there is an abrupt exponential rise in force that brings the tether out of the trap, indicating depletion of the membrane reservoir. In chick embryo fibroblasts and 3T3 fibroblasts, the maximum tether lengths that can be pulled at a velocity of 4 microm/s are 5.1 +/- 0. 3 and 5.0 +/- 0.2 microm, respectively. To examine the importance of the actin cytoskeleton, we treated cells with cytochalasin B or D and found that the tether lengths increased dramatically to 13.8 +/- 0.8 and 12.0 +/- 0.7 microm, respectively. Similarly, treatment of the cells with colchicine and nocodazole results in more than a twofold increase in tether length. We found that elevation of membrane tension (through osmotic pressure, a long-term elevation of tether force, or a number of transitory increases) increased reservoir size over the whole cell. Using a tracking system to hold tether force on the bead constant near its maximal length in the exponential phase, the rate of elongation of the tethers was measured as a function of tether force (membrane tension). The rate of elongation of tethers was linearly dependent on the tether force and reflected an increase in size of the reservoir. Increases in the reservoir caused by tension increases on one side of the cell caused increases in reservoir size on the other side of the cell. Thus, we suggest that cells maintain a plasma membrane reservoir to buffer against changes in membrane tension and that the reservoir is increased with membrane tension or disruption of the cytoskeleton.

Differences in F9 and 5.51 cell elasticity determined by cell poking and atomic force microscopy

We studied the elasticity of both a wild type (F9) mouse embryonic carcinoma and a vinculin-deficient (5.51) cell line, which was produced by chemical mutagenesis. Using cell poking, we measured the effects of loss of vinculin on the elastic properties of these cells. F9 cells were about 20% more resistant to indentation by the cell poker (a glass stylus) than were 5.51 cells. Using the atomic force microscope to map the elasticity of wild type and vinculin-deficient cells by 128 X 128 force scans, we observed a correlation of elasticity with cell poking elastometric measurements. These findings, as well as previous atomic force, rheologic, and magnetometric measurements [Goldmann and Ezzell, Exp. Cell Res. 226 (1996) 234-237; Ezzell et al., Exp. Cell Res. 231 (1997) 14-26], indicate that vinculin is an integral part of the cytoskeletal network.

Finite element implementation of anisotropic quasi-linear viscoelasticity using a discrete spectrum approximation

The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasilinear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament-tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

Investigating the cytoskeleton of chicken cardiocytes with the atomic force microscope

We have investigated living chicken cardiocytes with an atomic force microscope (AFM). Cytoskeletal structures like stress fibers can easily be imaged with the AFM. Here we have also measured the cell's elastic properties. By taking force curves as a function of lateral position (force mapping) we could compare the elastic properties at different locations of the same cell. In the lamellipodal region investigated here in detail, the elastic moduli range from around 10 up to 200 kPa on top of stress fibers. By degradation with cytochalasin B we can estimate to what extent the elastic properties of this type of cell are determined by the actin network.

Mechanical properties of cytoskeletal polymers

The mechanical properties of cytoplasm are dominated by microfilaments, microtubules, and intermediate filaments, collectively termed the cytoskeleton. This review discusses how the physical properties of these biopolymer systems are related to their molecular structures and interactions, and how remodelling of these biopolymers in vivo affects cell shape and motility.

Leukocyte biophysics. An invited review

The biophysical properties of leukocytes in the passive and active state are discussed. In the passive unstressed state, leukocytes are spherical with numerous membrane folds. Passive leukocytes exhibit viscoelastic properties, and the stress is carried largely by the cell cytoplasm and the nucleus. The membrane is highly deformable in shearing and bending, but resists area expansion. Membrane tension can usually be neglected but plays a role in cases of large deformation when the membrane becomes unfolded. The constant membrane area constraint is a determinant of phagocytic capacity, spreading of cells, and passage through narrow pores. In the active state, leukocytes undergo large internal cytoplasmic deformation, pseudopod projection, and granule redistribution. Several different measurements for assessment of biophysical properties and the internal cytoplasmic deformation in form of strain and strain rate tensors are presented. The current theoretical models for active cytoplasmic motion in leukocytes are discussed in terms of specific macromolecular reactions.